How to have consistent soft body physics in a specific area of an object using vertex groups?
I know this is an old post, but I thought I would contribute anyway. First you have to go into weight paint mode and paint the parts you would like to be rigid and assign this to a vertex group. This means that the parts you want to remain firm should be completely red. The parts that you want to be jiggly should be green or yellow, not completely blue (if it is blue, then it'll act like a cloth). Then go to the physics menu item on your object and add a new active rigid body and soft body. Under the soft body goal, turn the default goal strength up to 1 (this will make certain parts of the object completely rigid). Then, in the same area, set the vertex group to the weight painted group you made earlier. Bake the physics and play. PS. I'm working in blender 2.78